Nacho wrote:
>
> It is possible to do several variable limits in Mathematica 3.0?
>
Jens replied:
|
| Limit[Limit[x^2+y^2,x->0],y->0]
|
| works. But keep in mind that the order of limit's is *not* arbitarry!
|
The method above will often fail to identify cases where the Limit does not
exist.
However, I think the above will work where the function is continuous.
Consider the following example:
In[1]:= f[x_, y_]:= x y/(2 x^2 + y^2)
In[2]:= Limit [ Limit [ f[x,y], x->0 ], y->0 ]
Out[2]= 0
In[3]:= Limit [ Limit [ f[x,y], y->0 ], x->0 ]
Out[3]= 0
Both of the above suggest the Limit is zero.
However, ............
In[4]:= Limit[ f[x,y]/. x-> y/2, y->0]
Out[4]= 1/3
In[5]:= Limit[ f[x,y]/. x-> y/3, y->0]
Out[5]= 3/11
Since the result depends on how {x,y} are related as they approach {0,0}
we say the Limit does not exist.
The other day I sent in a different approach that as far as I can tell will
give the right answer for any problem it can handle. For the example above
my approach gives
Indeterminate.
Ted